Gwangju Institute of Science and Technology Intelligent Design and Graphics Laboratory Feature-Aware Filtering for Point-Set Surface Denoising Min Ki Park*Seung Joo LeeIn Yeop Jang Yong Yi Lee Kwan H. Lee Gwangju Institute of Science and Technology (GIST) Shape Modeling International 2013 (short paper)

Shape Modeling International 2013 /29 Contents  Introduction  Related work  The proposed method  Experimental results  Conclusion 2

Shape Modeling International 2013 /29 Introduction Point-based surface – No triangulation process – Simple and flexible data structure Measurement noise – Reflection, sensing error, misalignment of partial scans Denoising of a raw dataset is required 3 [Alexa01]

Shape Modeling International 2013 /29 Noise filtering Input surface(signal) – Additive noise Output surface(signal) – Noise free 4 Filtering

Shape Modeling International 2013 /29 Feature-preserving noise filtering Local averaging – Loss of salient features, details 5 Filtering

Shape Modeling International 2013 /29 Related work – Point-set surface denoising Umbrella operator [Pauly02] – Discrete Laplacian of a surface using an umbrella operator – Equal to isotropic diffusion Bilateral filtering [Fleishman03] – Height above surface is regarded as the grayscale intensity – Feature preservation using bilateral weights 6

Shape Modeling International 2013 /29 Related work – Point-set surface denoising Normal filtering [Jones04] – Normal improvement for smooth point rendering using spatial deformation Higher-order filtering [Duguet04] – Extend the bilateral filtering to second-order filtering – Surface curvature approximation using jet estimation 7

Shape Modeling International 2013 /29 Related work – Point-set surface denoising Robust moving least squares [Fleishman05; Őztireli09] – A novel MLS based surface definition via robust statistics – Outlier removal during surface reconstruction Non-local means [Guillemot12] – Improve feature preservation by exploiting self-similarities 8

Shape Modeling International 2013 /29 Problems of previous methods Fail to preserve sharp features during denoising process – Tangent discontinuity – Shallow feature – Highly curved surface Require a considerable computation time – Moving least squares surface reconstruction – Higher-order filtering via jet estimation 9

Shape Modeling International 2013 /29 Goal In this paper, we develop a fast and efficient denoising filter while preserving sharp features and small details 10

Shape Modeling International 2013 /29 Key idea Maintain multiple normals at the tangent discontinuity point after recognizing sharp features The second-order filter based on the curvature information 11

Shape Modeling International 2013 /29 Algorithm overview 12 Noisy surface Feature detectionNormal estimation Second-order filtering

Shape Modeling International 2013 /29 Feature detection Sharp feature detection via tensor voting [Park12] 13 : density : identity matrix : neighborhood : Straight line Spatial neighborhood N(p) Eigen-analysis

Shape Modeling International 2013 /29 Adaptive sub-neighborhood(ASN) 14 Tensor also encodes the local structure similarity ASN

Shape Modeling International 2013 /29 Normal estimation Smooth surface – Classical normal estimation (PCA) – Averaging the local neighborhood Normal at discontinuities – Maintain multiple normals of surface segments – Distance-based normal clustering 15 : Mahalanobis distance : Covariance matrix of all normals within ASN Tangent plane Abrupt change Tangent plane

Shape Modeling International 2013 /29 Vertex position update (previous) First-order surface approximation – [Fleishman03; Jones03; Sun07; Zheng11] – Projecting a point onto a local first-order predictor (tangent plane) – Accurate prediction for a plane, not for a highly curved surface 16 [Jones03]’s predictor [Fleishman03]’s predictor Noisy point Tangent plane of q Tangent plane of p

Shape Modeling International 2013 /29 Second-order prediction 17 Circle of curvature Predictor of p Predictor of p [Jones03]’s predictor [Fleishman03]’s predictor Noisy point

Shape Modeling International 2013 /29 Second-order prediction Second-order surface approximation 18 Our predictor Underlying surface Center of curvature

Shape Modeling International 2013 /29 Our prediction 19 Second-order approximationFirst-order approximation

Shape Modeling International 2013 /29 Proposed denoising filter 20 Spatial kernel Range kernel Predictor

Shape Modeling International 2013 /29 Results CAD-like model 21 Ground-truth Noisy modelBilateral filteringRIMLSOur method 10% Gaussian noise 20% Gaussian noise

Shape Modeling International 2013 /29 Results Free-form surface 22 Ground-truthNoisy modelBilateral filteringRIMLSOur method

Shape Modeling International 2013 /29 Results 23 ModelFandiskBunnyArmadillo Bilateral filtering RIMLS Proposed Bilateral filtering RIMLS Proposed 0% 15% ↑

Shape Modeling International 2013 /29 Comparison (6 algorithms) 24 * Results by MeshLab software [Cignoni]

Shape Modeling International 2013 /29 Comparison (6 algorithms) 25 * Results by MeshLab software [Cignoni]

Shape Modeling International 2013 /29 More results 26 Raw dataBilateral filteringRIMLS Proposed method

Shape Modeling International 2013 /29 Computation time Computation time of our method is comparable to the first-order filtering 27 * Intel i GHz CPU and 4GB RAM, no GPU

Shape Modeling International 2013 /29 Conclusion Novel second-order filtering for point-set denoising – Feature detection – Adaptive sub-neighborhood – Normal clustering – Feature-aware filtering The first- or second-order surface approximation Limitation – Dependent on the point normal estimates 28

Shape Modeling International 2013 /29 Thank you for your attention Q&A Intelligent Design and Graphics Laboratory Gwangju Institute of Science and Technology (GIST) Contact info. 29